Work Energy and Power - Result Question 64
67. A metal ball of mass $2 kg$ moving with a velocity of $36 km / h$ has a head on collision with a stationary ball of mass $3 kg$. If after the collision, the two balls move together, the loss in kinetic energy due to collision is [1997]
(a) $140 J$
(b) $100 J$
(c) $60 J$
(d) $40 J$
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Answer:
Correct Answer: 67. (c)
Solution:
- (c) Applying conservation of momentum, $m_1 v_1=(m_1+m_2) v$
$v=\frac{m_1 v_1}{(m_1+m_2)}$
Here, $v_1=36 km / hr=10 m / s$
$m_1=2 kg, m_2=3 kg$ $v=\frac{10 \times 2}{5}=4 m / s$
K.E. $(.$ initial) $=\frac{1}{2} \times 2 \times(10)^{2}=100 J$
K.E. $($ Final $)=\frac{1}{2} \times(3+2) \times(4)^{2}=40 J$
Loss in K.E. $=100-40=60 J$
